Question

A string of length $L$ is stretched by $\frac{L}{20}$ and speed of transverse wave along it is $v$. The speed of wave when it is stretched by $\frac{2L}{20}$ will be (assume that Hooke's law is applicable) :

• A. $2v$
• B. $\frac{v}{\sqrt{2}}$
• C. $\sqrt{2}v$
• D. $4v$

Answer 1

Answer: (C)

$\sqrt{2}v$

The relation of velocity of the wave and the change of the length of the wire is given by $v\propto \sqrt{\Delta L}$.

Here the total change in the length is $2L/20$.

Now, $v_1=v=k\sqrt{L/20}$, where $K$ is the proportionality constant.

Now, $v_2=k\sqrt{\left(2L/20\right)}=v\sqrt{2}$. (Using the value of $k$ from previous equation.)